Comparing adverbs of quantity∗

Jenny Doetjes, Utrecht Institute of Linguistics

jenny.doetjes@let.uu.nl

Draft, May 2002

Abstract

Starting out with some intriguing parallels and differences between French beaucoup ‘a lot’ and

souvent ‘often’, this paper develops an account of the distributional and semantic properties of four

classes of adverbial expressions of quantity: frequency adverbs (souvent), relative degree adverbs

(beaucoup), absolute degree adverbs ( un peu ‘a bit’) and x-times adverbs (trois fois ‘three times’).

These four classes are distinguished on the basis of two properties, which are defined in terms of the

type of quantity and quantification over ‘times’ or eventualities respectively. Souvent and beaucoup

correspond to relative quantities, while un peu and trois fois are absolute quantities. Souvent and trois

fois quantify over times, while beaucoup and un peu do not. The classification can account for a

number of properties of the four types of adverbs with respect to scope, selection, iteration,

habituality and the possibility of so-called relational readings. The paper focuses on French data, but

the same patterns can be found in other languages, such as for instance Dutch and English.

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1 Outline Adverbs of quantity (Q-adverbs) such as French beaucoup ‘a lot’ and souvent ‘often’ can have very similar meanings in some contexts while being radically different in other contexts (cf. Obenauer 1994 and Doetjes 1997). The sentences in (1a) and (1b), for instance, are practically synonymous. However, (1c) and (1d) have a very different interpretation. The pair in (1e,f) illustrates that there are even contexts in which souvent can be used while beaucoup is excluded. (1) a. Sylvie va beaucoup au cinéma. ‘Sylvie goes to the movies a lot’ b. Sylvie va souvent au cinéma. ‘Sylvie goes often to the movies.’ c. Sylvie a beaucoup apprécié ce film. ‘Sylvie liked this movie a lot.’ d. Sylvie a souvent apprécié ce film. ‘Sylvie often appreciated this movie.’

e. *Pierre a beaucoup acheté trois kilos d’olives1 ‘Pierre has bought three kilos of olives a lot’

f. Pierre a souvent acheté trois kilos d’olives. ‘Pierre has often bought three kilos of olives.’

In this paper I will make a detailed comparison between beaucoup and souvent in order to understand why they are so similar in some contexts and so different in others. The opposition between beaucoup and souvent is not restricted to these two lexical items. Both are representatives of a class. Beaucoup is a member of a rather large class of degree adverbs, including also trop ‘too much’ and énormément ‘a whole lot’. Souvent is a frequency adverb, and as such belongs to the same class as rarement ‘seldom’. It turns out that the behaviour of souvent and beaucoup can be much better understood when they are compared with x-times adverbs such as trois fois.2 Moreover, the class of degree adverbs is not homogeneous: I will make a distinction between relative degree adverbs such as beaucoup and absolute degree adverbs such as un peu ‘a bit’. The division between the four classes (frequency adverbs, the two types of degree adverbs and x-times adverbs) will be made on the basis of two criteria. The first criterion is the type of quantity that is expressed by the Q-adverb. This can be an absolute quantity, as is the case for three times and un peu, or a relative quantity, as is the case for often and beaucoup. I will refer to this as [±RQ], where RQ stands for Relative Quantity. The second criterion is whether the Q-adverb introduces an iterative reading. This will be referred to as [±QT], where QT stands for quantification over times. Q-adverbs that have this property say something about the number of times an event or a situation took place. Degree adverbs will be analysed as [–QT] while frequency adverbs and x-times adverbs are [+QT]. I will mainly concentrate on French, but the classification can be extended to other languages, such as Dutch and English. In what follows the division between the four classes on the basis of these two properties will be further motivated. It will be shown how these properties are correlated with certain aspects of the distribution of these items. The property [+RQ] correlates, for instance, with the possibility to use an expression in habitual contexts (cf. (1a)). [–QT] turns out to correlate with the impossibility to take wide scope (cf. (1c)), and with the possibility to be used as a determiner (as in beaucoup de livres ‘a lot of books’). The combination of [+RQ] and [+QT] will be shown to be necessary in order to obtain a so-called relational reading, in which the restriction of the Q-adverb is determined by a when-clause or another adverbial expression.

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This turns out to be the source of the contrast in (1e,f). The similarity in interpretation between beaucoup and souvent in (1a,b) will be argued to be the result of the shared caracteristic [+RQ] on the one hand, and very specific property of the context on the other, as a result of which [–QT] expressions become similar to [+QT] expressions. 2 Four classes of Q-adverbs 2.1 Quantification over times If we look more closely to the meaning of the four types of expressions introduced above, we observe that souvent and trois fois are necessarily iterative, in the sense that they say something about the number of times an event takes place. Beaucoup and un peu, on the other hand, do not necessarily indicate the number of times an event took place. Consider the examples in (2): (2) a. Il a plu beaucoup. it has rained a-lot

b. Il a plu un peu. it has rained a bit

c. Il a plu souvent. it has rained often

d. Il a plu trois fois. it has rained three times

For (2a) to be true, we need a situation in which there is a lot of rain, but it does not need to rain many times. In fact, the sentence can be used in situations where it has rained continuously for a long period. In (2b) we find something similar. It is the global amount of raining that counts, not the number of showers. The examples in (2c) and (2d), on the other hand imply iteration: they say something about the number of raining events or the number of times that it rained. The difference between the two types of interpretation is particulary clear in the following example, which I heard in the south of France. A woman farmer complained about the dry weather, uttering the sentence in (3): (3) Il a plu souvent, mais il n’a pas plu beaucoup. it has rained often but it NEG-has not rained a-lot I will refer to this contrast in terms of the property QUANTIFICATION OVER TIMES or QT. Expressions such as souvent (frequency adverbs) and trois fois (x-times adverbs) are [+QT], and specify the number of times something happened. In most cases, [+QT] will amount necessarily in an iterative reading (an exception to this will be discussed in section 4.2 below). Degree adverbs such as beaucoup and un peu are not inherently iterative. We will get back to the opposition between [+QT] and [–QT] in more detail in section 3. 2.2 Relative versus absolute quantity

In the literature on Q-adverbs, an often discussed difference is the one between souvent and trois fois (see Hoepelman & Rohrer 1981, De Swart 1991). This difference is illustrated in (4):

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(4) a. La semaine dernière/pendant sa jeunesse, Pierre est souvent allé au Louvre.

‘Last week/during his youth, Pierre went often to the Louvre.’ b. La semaine dernière/ pendant sa jeunesse, Pierre est trois fois allé au

Louvre. ‘Last week/during his youth, Pierre went three times to the Louvre.’

The number of times corresponding to souvent varies with the time interval we pick. Four times may qualify as often for the period of a week, but if we are talking about the much longer period of Pierre’s youth, four times is not what we would call often. If we turn now to the examples with trois fois ‘three times’ it is clear that the time interval does not play a role whatsoever in interpreting the x-times adverb. Q expressions such as often will be called expressions of RELATIVE QUANTITY and have the property [+RQ], where RQ stands for ‘relative quantity’. These expressions are not interpreted in an absolute sense, but always depend for their interpretation on a contextually given ‘quantity of reference’. In the examples in (4), this quantity of reference corresponds to the number of times we would normally expect Pierre to go to the Louvre in a week or in a year, depending on the time interval we pick. The use of souvent indicates that the number of times Pierre went to the Louvre exceeds this quantity of reference. Trois fois on the other hand, is [–RQ], and corresponds to an absolute quantity. Its interpretation does not depend on a contextually given ‘quantity of reference’. As a result the number of times indicated by trois fois does not depend on contextual factors such as the time interval. Given this definition there are many expressions that we expect to be [+RQ]. Not only other frequency adverbs such as plus souvent ‘more often’, but also degree adverbs such as beaucoup and davantage. In all of these cases, the quantity is determined with respect to a contextually given quantity of reference:

(5) a. La semaine dernière/ Pendant sa jeunesse, Pierre est allé plus souvent au Louvre que Jean. ‘Last week/ during his youth, Pierre went to the Louvre more often than Jean did.’

b. La semaine dernière/ l’année dernière, Pierre est beaucoup allé au Louvre. ‘Last week/ last year, Pierre went to the Louvre a lot.’

c. La semaine dernière/ l’année dernière, il a plu davantage à Paris qu’à Amsterdam.

‘Last week/ last year, it rained more in Paris than in Amsterdam.’ In (5a), the quantity of reference is the number of times Jean went to the Louvre during the interval we are talking about. This number of times varies depending on the time interval we pick. The number of times indicated by plus souvent is defined as ‘more than n times’, where n corresponds to the quantity of reference. As such, it varies depending on the time interval. Beaucoup and davantage are similar to souvent and plus souvent, and can be seen as their [–QT] counterparts. All frequency adverbs and most degree adverbs have the property [+RQ], as shown in the overview at the end of this section. The example in (6) shows that x-times expressions containing a vague indication of the number of times are [–RQ] as well. Quelques fois ‘a small number of times’ and plusieurs fois ‘several times’ are vague, but they are not dependent on a contextually given quantity of reference.3 Quelques fois can be defined as ‘a small number of times’, and plusieurs fois as ‘more than once’. As such, we expect them to be independent of the time interval we pick, on a par with trois fois, which is correct:

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(6) La semaine dernière/ Pendant sa jeunesse, Pierre est quelques fois/ plusieurs fois allé

au Louvre. ‘Last week/ during his youth, Pierre went to the Louvre a few times/several times.’ Whereas beaucoup is the [–QT] counterpart of souvent, the degree adverb un peu could be characterised as the [–QT] counterpart of quelques fois ‘a small number of times’. As such, we expect un peu to be [–RQ] which means that it is not interpreted with respect to a contextually given quantity of reference that may vary with the time interval we pick. The examples in (7) show that this is in fact the case: (7) a. Entre midi et deux heures, Pierre a dormi un peu.

‘Between noon and two o’clock, Pierre slept a bit.’ b. Pendant la journée, Pierre a dormi un peu. (‘during the day’) c. Pendant le weekend, Pierre a dormi un peu. (‘during the weekend’) d. StrangeLa semaine dernière, Pierre a dormi un peu. (‘last week’) e. Very strangeL’année dernière, Pierre a dormi un peu. (‘last year’)

With respect to these examples we can make two observations. In the first place the sentence in (7a), where the time interval is very short, does not exclude a situation in which Pierre sleeps during a very large proportion of this time interval (one and a half hour for instance). In the second place, the sentences become strange when the time interval is getting larger. Sleeping a bit during a day or a weekend is possible. However, the amount of sleep one needs in a week or a year exceeds the quantity we can refer to by using un peu. These examples illustrate that vague Q adverbs such as un peu are not completely context independent, as is trois fois. Rather, they could be qualified as ‘weakly context dependent’. Comparing (7b) and (7c), we will tend to interpret un peu as more in (7c). The strangeness of (7d) and (7e) and the fact that the interpretation in (7a) is completely independent of the time interval shows that this weak context dependency is different from the stronger effect of context we observed for [+RQ] expressions. This stronger effect is what we are interested in here, and is ascribed to the interpretation of the Q adverb with respect to a contextually given quantity of reference. The weak influence of context exemplified in (7b) and (7c) seems to be due to a combination of vagueness and world knowledge. Vagueness allows for a certain range of possible interpretations, and context/ world knowledge plays a role in the way we interpret the vague expression. In the examples (4) to (7) we used dependency on a time interval as a test for distinguishing [±RQ] expressions. It has to be stressed that we are talking about a more abstract property which makes dependency on the time interval possible or impossible: the presence/absence of a contextually determined quantity of reference as part of the meaning of the Q expression. It is important to notice that in the examples discussed so far, the interpretation of [+RQ] expressions depends on the choice of the time interval because the quantity of reference is interpreted in the scope of the time interval. However, this is not necessarily the case. It is also possible that the quantity of reference is outside of the scope of the time interval, in which case the [+RQ] expression becomes independent on the choice of the time interval, on a par with [–RQ] expressions. Consider the example in (8):

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(8) a. La semaine dernière/ Pendant sa jeunesse, Pierre est allé plus souvent au Louvre que son grand-père y est allé pendant toute sa vie.

‘Last week/ during his youth, Pierre went to the Louvre more often than his grandfather did during his whole life.’

b. La semaine dernière/ l’année dernière, il a plu davantage à Paris qu’il n’a plu à Amsterdam depuis un an et demi. ‘Last week/ last year, it rained more in Paris than in Amsterdam during the past one and a half years.’

In (8a), the quantity of reference with respect to which plus souvent is interpreted (the number of times Pierre’s grandfather went to the Louvre during his whole life) is outside of the scope of the time interval in the matrix sentence. As a result, the quantity corresponding to the [+RQ] expression plus souvent is the same whether we use la semaine dernière or pendant sa jeunesse. The same effect obtains for davantage in (8b). As a result, the sentence becomes very unlikely when we choose the short time interval la semaine dernière ‘last week’, an effect which does not obtain in (5c), where davantage and the quantity of reference with respect to which it is interpreted are within the scope of the same time interval. On the other hand, [–RQ] expressions can be made dependent on a time interval by adding a modifier of the type par semaine ‘per week’ or tous les après midi ‘every afternoon’ (cf. de Swart 1991): (9) a. L’année dernière/ pendant sa jeunesse, Pierre est allé au Louvre trois fois

par semaine. ‘Last year/during his youth, Pierre went three times per week to the Louvre.’

b. L’année dernière, Pierre a dormi un peu tous les après-midi. ‘Last year, Pierre slept a bit every afternoon.’

In (9a), the number of times corresponding to the complex Q trois fois par semaine depends on the choice of the time interval. The example in (9b) is not strange; (7d), in which un peu is not modified, is.4 On the basis of the two properties introduced above, we can distinguish four classes, some examples of which are given in the schema below. Informal descriptions corresponding to their meanings are added, which make clear why they belong to a certain category rather than to another (for a more extensive overview of degree adverbs, cf. Doetjes 1997 and Doetjes, Neeleman & Van de Koot 1998). The bold faced members are used in this paper as prototypical members, unless reference to other members of the class is necessary.

[+RQ],[+QT],: frequency adverbs

souvent rarement plus souvent trop souvent

more than n times, where n is contextually determined by a norm/what we expect less than n times, where n is contextually determined by a norm/what we expect more than n times, where n is contextually given, usually explicitely in a que ‘than’-phrase more than n times, where n is contextually defined as the maximal quantity that is appropriate

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[+RQ], [–QT]: relative degree adverbs

beaucoup peu davantage trop

more than n, where n is contextually determined by a norm/ what we expect less than n, where n is contextually determined by a norm/ what we expect more than n, where n is contextually determined, usually explicitely in a que phrase more than n, where n is contextually defined as the maximal quantity that is appropriate

[–RQ], [+QT]: x-times adverbs

trois fois plusieurs fois quelques fois

at least or exactly three times more than once a small number of times

[–RQ], [–QT]: absolute degree adverbs

un peu un tantinet

a small quantity a small quantity

The class of frequency adverbs also includes toujours ‘always’. Toujours should be characterised as a relative quantity because the number of times it describes depends on the cardinality of the set of eventualities defining the restriction of toujours. This restriction varies, among others, with the time interval we pick. We will come back to a number of special properties of toujours below. Note that all members of the class of absolute degree adverbs have roughly the same interpretation (‘a bit’, ‘a little’). This can be understood when we compare this class to the other class of [–RQ] expressions, the x-times adverbs. We can observe that un peu (or either one of its near synonyms) is the counterpart of quelques fois. All other members of the class of x-times adverbs contain cardinals. We do not expect the counterparts of NUMERAL fois and plusieurs fois in the class of absolute degree adverbs, because these do not involve counting of a number of times. Counting is incompatible with the [–QT] nature of un peu. 2.3 Predictions Given the way we defined the four classes of adverbs of quantity in terms of the two properties [±RQ] and [±QT], we expect to find parallels and differences between the four classes of Q expressions. More specifically, we make the following predictions: 1. Souvent and trois fois can be opposed to beaucoup and un peu in contexts where

quantification over times plays a role. 2. Souvent and beaucoup can be opposed to trois fois and un peu in contexts where the

opposition between relative quantity and absolute quantity plays a role. 3. Beaucoup, un peu and trois fois can be opposed to souvent in contexts that require both

relative quantity and quantification over times. In these contexts only souvent, which has both properties, will be allowed. Beaucoup and un peu will be excluded because they lack iteration, while trois fois is excluded because it does not indicate a relative quantity.

As for the first prediction, the property [±QT] correlates with several other properties, which will be extensively discussed in section 3.

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In the first place, it turns out that expressions which are [–QT] can always be used as determiners, while this is excluded for the expressions which are [+QT]: (10) a. Il y a [un peu/ beaucoup de vin]. there is a bit/ a lot of wine

b. *Il y a [souvent/ trois fois (de) vin]. there is often/ three times of wine

Expressions such as beaucoup and un peu are not restricted to purely adverbial contexts. They can always function as determiners, and often also as degree modifiers in the adjectival domain (cf. un peu in un peu fatigué ‘a bit tired’). The second difference has been briefly mentioned above. Expressions that are [+QT] usually have an inherently iterative reading, while expressions that are [–QT] do not. Whereas souvent corresponds to ‘many times’, beaucoup rather indicates a large quantity in a global way. Finally, we can observe that only those expressions that are [+QT] can take scope over an indefinite (cf. also (1c,d)): (11) a. Il a souvent acheté deux kilos d’olives. he has often bought two kilos of-olives ‘He often bought two kilos of olives.’

b. Il a trois fois acheté deux kilos d’olives. c. *Il a beaucoup acheté deux kilos d’olives d. *Il a un peu acheté deux kilos d’olives

Whereas souvent and trois fois can take scope over the direct object deux kilos d’olives, this is not possible when we use beaucoup or un peu. I will show below that these three differences can be related to each other, and that they derive from the presence/ absence of quantification over times. Section 4 concentrates on the second prediction. Only [+RQ] expressions can be used in habitual contexts (cf. also (1a,b)). In accordance with the second prediction, this sets apart souvent and beaucoup on the one hand and trois fois and un peu on the other: (12) a. Jean dort souvent/beaucoup. Jean sleeps often/a-lot ‘Jean has the habit of sleeping often/a lot.’ b. #Jean dort trois fois. ‘Jean has the habit of sleeping three times.’ c. Jean dort un peu. ‘Jean is half asleep

NOT : ‘Jean has the habit of sleeping now and then.’ The example in (12b), contrary to the one in (12a), does not have a habitual reading. As we will see, this property has to do with the possibility to interpret [+RQ] expressions depending on the choice of a time interval. According to the third prediction, there might be contexts where an expression needs to be both [+QT] and [+RQ]. In that case, only souvent-type expressions will be allowed, while the

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other three types of expressions are excluded. An example of such a contrast is the relational reading. Relational readings will be treated in detail in section 5. Consider the example in (13): (13) Quand il est à Paris, Pierre va souvent au Louvre.

when he is in Paris, Pierre goes often to-the Louvre This sentence has two readings. In the first reading, it says that whenever Pierre is in Paris, he goes often to the Louvre. In the second reading, Pierre goes to the Louvre at least once at most of the occasions that he is in Paris. This second reading is called the relational reading (cf. de Swart 1991). The other three types of expressions only allow for nonrelational readings when used in this context: (14) a. Quand il est à Paris, Pierre va beaucoup au Louvre.

when he is in Paris Pierre goes a lot to-the Louvre ‘Whenever he is in Paris, Pierre goes to the Louvre a lot.’ b. Quand il est à Paris, Pierre va trois fois au Louvre.

‘Whenever he is in Paris, Pierre goes three times to the Louvre.’ c. Quand il est à Paris, Pierre se promène un peu.

when he is in Paris, Pierre self walks a bit ‘Whenever he is in Paris, Pierre walks a bit.’

The impossibility of relational readings in the context of trois fois and un peu will turn out to be related to the impossibility to use these expressions in nonhabitual contexts. As a result all expressions that are [–RQ] are excluded. The impossibility of beaucoup in this context shows, however, that the absence of the relational reading cannot simply be a matter of the opposition between relative and absolute quantity. I will argue that the opposition between (13) and (14a) is due to the fact that beaucoup is [–QT]. The property [+QT] turns out to be an additional prerequisite for inducing the relational reading. As such the relational reading presents a context in which the third prediction is borne out. 3 [±QT]: souvent / trois fois vs beaucoup / un peu 3.1 Quantification over times X-times adverbs such as trois fois ‘three times’ typically contain the element fois ‘times’. We find this type of element in the Dutch and English counterparts of the x-times adverbs as well (cf. English three times and its Dutch counterpart drie keer). When looking at the morphology of souvent-type expressions, we can observe that these often (though not always) contain morphological material that corresponds to something like fois or times. The presence of @ indicates that the form is archaic. (15) a. quelquefois; parfois; @maintefois; [French] sometimes by-time (‘sometimes’) many-times plus d’une fois more than once (‘regularly’) b. dikwijls; menigmaal; @dikmaal(s) [Dutch] many-while+GEN many-time many-time(GEN) c. sometimes; @oft(en)times; @oftenwhile [English] In expressions such as beaucoup and un peu, however, we never find elements corresponding to fois.5

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I will adopt the hypothesis according to which all frequency expressions, whether they are morphologically complex or not, are semantically complex in the sense that they contain a Q element and a restriction, which corresponds to the element fois ‘times’ in trois fois. As for frequency expressions such as souvent, this means that we follow in essence Von Fintel’s (1994) hypothesis according to which adverbs of quantification quantify over situations and contain a hidden domain anaphor. I take this domain anaphor to be an abstract fois.6 (16) a. souvent (Q+restriction): Q (abstract many): [restriction abstract fois] [nuclear scopeVP/IP]

b. trois fois: trois: [restriction fois] [nuclear scopeVP/IP] Expressions that are [−QT] consistently lack such a restriction. As a result they are not quantifying over times. I claim that they function as degree expressions and, as such, they measure the quantity expressed by the VP predicate. In for instance il a plu beaucoup ‘it rained a lot’, the predicate pleuvoir ‘to rain’ leaves open how much it has rained. Beaucoup indicates that the quantity of raining exceeds a certain amount corresponding to what we expect (the quantity of reference). In (17a), the predicate aller au Louvre ‘to go to the Louvre’ indicates that there has been one or more going to the Louvre events.7 Beaucoup indicates in this sentence that the number of going to the Louvre events expressed by the predicate is rather high. Similarly, un peu in (17b), indicates that the quantity of walking expressed by the predicate se promener is rather small. (17) a. Sylvie est beaucoup allé au Louvre. ‘Sylvie went to the Louvre a lot.’ b. Pierre s’est promené un peu. ‘Pierre walked a bit.’ In what follows, I will discuss a number of properties that correlate with [±QT], and show how they can be accounted for. 3.2 Compatibility with other categories Contrary to souvent and trois fois, beaucoup and un peu can be used in nominal contexts, where they have exactly the same function as in verbal contexts. They indicate the degree of quantity corresponding to the noun they modify: (18) a. beaucoup de livres. ‘a lot of books’ b. beaucoup de soupe ‘a lot of soup’ c. un peu de soupe ‘a bit of soup’ In these cases, beaucoup and un peu are similar to determiners such as plusieurs ‘several’. Souvent and trois fois, on the other hand, are always adverbial, and cannot indicate quantity with respect to a nominal expression: (19) *souvent/trois fois (de) livres/ de soupe often/three times (of) books/ soup

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Many degree adverbs, including un peu, can be used to modify adjectival projections as well. Beaucoup is an exception to this generalization (cf. Doetjes 1997, 2001a,b). Assez ‘enough, quite’ and moins ‘less’, are examples of [+RQ] degree adverbs that can be used in adjectival contexts: (20) assez/moins/un peu difficile quite/ less/ a bit difficult When used with adjectives, these expressions resemble degree words that are found in the context of adjectives, such as très ‘very’, aussi ‘as’. Compare for instance English too, which only combines with adjectives and French trop ‘too, too much’. When combined with an adjective it translates as ‘too’ and when combined with an NP or a VP it translates as ‘too much/many’: (21) a. trop de livres too many books

b. Pierre parle trop Pierre talks too-much

c. trop difficile too difficult

The generalization one can make about the contexts in which degree adverbs such as beaucoup, trop and un peu can be used, is that the modified phrase must introduce a scale. In the case of NPs this is a quantitative scale: when using the plural books or the mass noun soup, the number of books or the amount of soup may vary on an ascending scale. The noun books can be used to refer to any number of books, while the noun soup can be used to refer to any quantity of soup. Link 1983 and Krifka 1992 (among others) define this property in terms of cumulative reference in a lattice theoretic framework. In this framework, the denotation of books corresponds to all possible sets of more than one book, which are partially ordered in a join semilattice by the part of relation (each of the possible sets of two books is the subset of a number of possible sets of three books and so forth). Similarly soup corresponds to all possible masses of soup. The predicates books and soup have cumulative reference because the following holds: (22) ∀P (CUM(P) ↔ ∀x,y[P(x) & P(y) → P(x ∨ y)] A predicate P has cumulative reference iff for every x and for every y that have the property P, the join of x and y (x ∨ y) has the property P as well, where the join of x and y corresponds, roughly speaking, to x and y put together. This property holds for plurals and mass nouns, but not for count singulars. Count singulars denote a set of singularities. Typically, it is not possible to use degree expressions with a singular count noun, which does not introduce a quantitative scale: Beaucoup de théière ‘a lot of tea pot’ is excluded, unless we would manage to assign a mass interpretation to the singular théière ‘tea pot’.8 This view can be extended to the adverbial use of beaucoup. Following Bach (1986), verbal predicates can be taken to be the counterparts of plural, singular or mass nominal predicates. A predicate such as to rain is a mass predicate, while to go to the movies corresponds to a count predicate, which is ambiguous between a singular or a plural reading. ‘Once only’ predicates such as to write the letter (where the letter is a token) cannot be interpreted as a plural predicate, and could therefore be compared to singular count nouns.

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The adverbial use of beaucoup is possible in contexts where the VP allows for either a plural or a mass interpretation. In these cases the predicate introduces a quantitative scale similar to the one found in plural and mass nouns: (23) a. beaucoup de livres [Plural count NP/VP] a-lot of books b. Jean va beaucoup au Louvre. Jean goes a-lot to-the Louvre c. beaucoup de soupe [Mass NP/VP] a-lot of soup d. Il a plu beaucoup it has rained a-lot e. #beaucoup de théière [Singular count NP/VP] a-lot of teapot f. #Jeanne a beaucoup écrit la lettre. Jeanne has a-lot written the letter In both the nominal and the verbal domain we find beaucoup in abstract contexts. In these cases the scale does not seem to be a quantitative one, but a qualitative one. Consider for instance the examples in (24). In (24a), beaucoup expresses the intensity of the pleasure, and in (24b) the intensity of the appreciation. The example in (24b) is due to Obenauer (1983,1984). I will come back to the effect of the verbal predicate on the interpretation of beaucoup in section 4.3. (24) a. avec beaucoup de plaisir with a-lot of pleasure ‘with great pleasure’ b. J’ai beaucoup apprécié ses conseils.

‘I appreciated his advice a lot.’

When degree adverbs combine with adjectives, they also depend on the presence of a scale. Nongradable adjectives such as dernier ‘last’ cannot be modified by these expressions (*moins dernier). The scale introduced by these adjectives is obviously not a quantitative one. In these contexts moins, trop, and un peu indicate a qualitative degree or intensity, as in the examples in (24). A pure degree interpretation in which no quantity is involved is completely excluded for [+QT] expressions such as souvent and three times. This follows from the hypothesis according to which they both contain the (overt or covert) restriction ‘times’. Summarizing, we have seen that beaucoup and un peu are not restricted to adverbial contexts. They function as degree modifiers in verbal, nominal, and often also adjectival contexts alike. As for their selectional properties, we can state that they are sensitive to the presence of a scale which can be either quantitative or qualitative in nature. This scale can be provided by expressions of different categories, as a result of which expressions such as beaucoup and un peu can be used as modifiers of different categories. Depending on the context, they will indicate a degree of quantity or an intensity. Souvent and three times state something about a number of times something happened. This makes them truly adverbial in nature, as a result of which they can neither be used as determinerlike elements nor as degree modifiers in adjectival and adverbial contexts.

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3.3 Iteration The property [+QT] is the source of the inherently iterative reading of souvent and trois fois.9 While souvent is inherently iterative, beaucoup is not. In certain contexts, however, there does not seem to be much difference between beaucoup and souvent. This leads easily to the assumption that beaucoup is ambiguous, and has a reading which is inherently iterative as well. Given the claim that the inherent iterative reading of souvent is directly due to the property [+QT] and is correlated with a number of other properties that beaucoup lacks, an analysis of beaucoup in terms of ambiguity is not attractive. It turns out that it is much more plausible to analyse the cases of I ‘iterative’ beaucoup as a contextual effect evoked by a plural interpretation of the verbal predicate. This analysis allows us to maintain the hypothesis according to which beaucoup is unambiguous. The examples in (25) illustrate the similarity of beaucoup and souvent: (25) a. Sylvie va beaucoup au cinéma. (=(1a,b)) ‘Sylvie goes to the movies a lot.’ b. Sylvie va souvent au cinéma. ‘Sylvie goes often to the movies.’ These sentences are judged to be synonymous. Some speakers, however, assign to (25a) a second reading that (25b) lacks. Beaucoup can modify the number of visits, but it can also be used to stress that someone has spent a lot of time in the cinema. As in the ‘rain’-example in (3), repeated here in (26), beaucoup can be used to refer to the global quantity, while souvent cannot. (26) Il a plu souvent, mais il n’a pas plu beaucoup. (=(3)) it has rained often but it NEG-has not rained a-lot The global, noniterated, reading is much more straightforward for (26) than for (25). This has to do with the nature of the predicate. Predicates such as pleuvoir ‘to rain’ are similar to mass nouns (water, rain). Mass nouns refer to unbounded entities, while mass predicates refer to unbounded situations. Predicates such as aller au cinéma ‘to go to the movies’ constitute count predicates and can have a plural interpretation, as I argued in the previous section. The combination of beaucoup and a plural predicate results in a reading which is similar to the iterative reading of souvent, but which is crucially not identical. In the case of beaucoup, we make use of the plurality of the predicate. In beaucoup aller au cinéma we define a set of sets of visits to the cinema the cardinality of which exceeds the quanitity of reference n, where n corresponds to what we expect in a given context. In the case of souvent, we do not make use of the plurality of the predicate (this will be further motivated in the next section). Rather, souvent specifies that the cardinality of the set of singular visits to the cinema by Sylvie is a rather large one. In this approach the iterative reading of a sentence containing beaucoup is not connected to the meaning of beaucoup but to the meaning of the predicate. In this light it is interesting to look at the second reading that some speakers assign (25a). The second reading can be understood if we assume that these speakers allow the predicate aller au cinéma to shift to a mass interpretation. As a result, the sentence in (25b) does not necessarily refer to a high number of cinema visits, but can also describe a large amount of time spent in the cinema watching movies. Similarly, Il a plu beaucoup can be used in a context where there have been a lot of showers. This is not very plausible in (26), as this sentence would be a contradiction. However, the reading seems to be possible in other contexts. Instead of assuming that beaucoup is ambiguous, I propose that in this case the predicate pleuvoir shifts from a mass to a count interpretation. This

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allows us to conclude that beaucoup has never a ‘many times’ reading, and does not have a reading in which it is synonymous with souvent. The shifting processes described above are very similar to the ones we find in the nominal system, which were already briefly mentioned in the previous section. In the nominal domain shifts from a mass to a count interpretation and vice versa are very common. The mass noun vin ‘wine’, for instance, can be used as a count noun in cases such as Nous servons trois vins blancs ‘We serve three white wines/ types of white wine’. On the other hand, count nouns such as pomme can be used as mass nouns in cases such as Il faut ajouter un peu de pomme à la salade ‘One should add some apple to the salad’. In the nominal system, beaucoup can be combined with a singular mass noun or with a plural count noun. In case the noun has a count interpretation, beaucoup can be replaced by un grand nombre ‘an important number’. When it combines with a mass noun, it can be replaced with une grande quantité ‘a big amount’. The difference between these two ‘readings’ does not seem to be a matter of ambiguity, as it is purely dependent on the predicate. (27) a. beaucoup de vin/vins a-lot of wine/wines

b. beaucoup de pommes/pomme a-lot of apples/apple

Beaucoup always corresponds to a large quantity, and the illusion of ambiguity is the result of different predicates with which beaucoup is combined. In the same way, the iterated reading of sentences containing adverbial beaucoup can be attributed to the count nature of the predicate. Contrary to what we see in the nominal system, plurality of events is not marked morphologically in the verbal system. The interpretive difference between a mass and a count predicate in the verbal system does not correlate with morphological marking. However, the possibility of mass and count interpretations accounts for the way adverbial beaucoup is interpreted in the same way as in the nominal system. We can conclude then, that iteration in the case of beaucoup is not due to lexical ambiguity of beaucoup itself, but depends entirely on the context. This is corroborated by the observation I made about degree adverbs in the combination with abstract nouns and verbs or adjectives (cf. (20) and (24)). In these cases as well the nature of the scale yields the illusion of a different reading of the degree expression, which can be traced back to the context. In brief, beaucoup and other degree adverbs are interpreted with respect to a scale. This scale is provided by the predicate. Depending on the predicate, beaucoup indicates a large global amount, a high number or a high intensity. Souvent, on the other hand is inherently iterative, which means that it always has a ‘many-times’-interpretation, independently of the mass/count properties of the predicate. Moreover, as we have seen in the preceding section, it never has an intensity reading in the context of scalar predicates (cf. Il l’apprécie souvent ‘He often appreciates it’, not ‘He appreciates it a lot’). Both observations are not surprising if we take into account the present proposal: souvent is in fact composed of a Q and an abstract restriction introducing ‘times’. The presence of this abstract restriction predicts the inherent iterative nature of frequency expressions. 3.4 Scope effects A striking difference between beaucoup and souvent is that only the latter can take scope over an indefinite. The impossibility of assigning wide scope to beaucoup with respect to an indefinite, even in contexts where beaucoup is in a higher position than the indefinite, has

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already been noticed by Milner (1978), who discusses the contrast in (28) (cf. also Moltmann 1998 for German): (28) a. Trois Allemands sont beaucoup venus chez toi l’an dernier. three Germans are a-lot come at your-place the-year last ‘Three Germans visited you a lot last year.’ b. *Il est beaucoup venu trois Allemands chez toi l’an dernier. it is a-lot come three Germans at your-place the-year last ‘Last year, there came three Germans to your place a lot.’ In the sentence in (28a), a specific reading of the subject trois Allemands ‘three Germans’ is obligatory. The Q-expression beaucoup cannot have scope over the subject. This cannot be due to the position of the subject with respect to beaucoup only. In (28b), where beaucoup occupies a higher position than the indefinite, the narrow scope reading of the object is excluded as well. As the impersonal construction does not allow for a specific reading of the subject, the sentence is ruled out. If we compare the behaviour of beaucoup with that of souvent, it is immediately clear that souvent can take scope over the subject in an impersonal construction as in (29b). Wide scope of souvent over a subject is rather restricted, so the subject of (29a) will be interpreted outside of the scope of souvent (cf. Obenauer 1994 for a discussion of examples where souvent does take wide scope over an indefinite subject): (29) a. Trois Allemands sont souvent venus chez toi. three Germans are often come at your-place ‘Three Germans visited you a lot last year.’ b. Il est souvent venu trois Allemands chez toi.

it is often come three Germans at your-place ‘There often came three Germans to your place.’ The difference between souvent and beaucoup is systematic. Consider for instance the following examples (cf. (1c,d) and (11)): (30) a. *Jean achète beaucoup deux kilos d’olives. Jean buys a-lot two kilosof-olives ‘Jean buys two kilos of olives a lot.’10 b. Jean achète souvent deux kilos d’olives. Jean buys often two kilos of-olives ‘Jean often buys two kilos of olives.’ Un peu is in this respect similar to beaucoup. It can not take scope over an indefinite. Trois fois, on the other hand, is like souvent in that it easily takes scope over an indefinite: (31) a. *Jean a un peu acheté deux kilos d’olives. Jean has a bit bought two kilos of-olives

b. Jean a trois fois acheté deux kilos d’olives. Jean has three times bought two kilos of-olives We can conclude that the possibility to have wide scope over an indefinite correlates with the property [+QT]. As I have argued above, expressions which are [+QT] have in common that they are complex in the sense that they contain both a Q element and a restriction. This

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restriction is abstract in the case of souvent, and overtly realized as fois in the case of trois fois. Degree expressions, which are [–QT], do not contain a restriction (see (16) and (17) above). Let us first examine the reason why beaucoup and other [–QT] expressions cannot take wide scope over an indefinite. As I argued above, beaucoup operates on the meaning of a predicate, which has to be interpretable as a scale. In the case of NPs and VPs this scale corresponds either to the global quantity of a mass predicate, or to the plural quantity of a count predicate. Expressions such as beaucoup cannot be combined with singular NPs because these correspond to a specific quantity, not to a scale. As I have argued above, #beaucoup de théière is strange, because beaucoup forces a mass interpretation of théière and such an interpretation is hard to get. Given this, we expect that modification of a singular count VP is excluded as well.11 This offers an explanation for the scope properties of beaucoup. The presence of an indefinite blocks a plural reading of the predicate, unless the indefinite is interpreted referentially. Only then, the predicate can be understood as a plural predicate. Consider two events in which two kilos of olives are bought. It is not possible to refer to this plural event by using the predicate acheter deux kilos d’olives ‘to buy two kilos of olives’, because the total amount of olives that has been bought does not correspond to two kilos but to four kilos. In case the indefinite is referential, a plural interpretation of the predicate is predicted to be possible, as then the problem does not arise. Given that the referential reading is not very likely in the case of the indefinite deux kilos d’olives in the examples (30a), the predicate acheter deux kilos d’olives resists modification by beaucoup. Predicates which may have a plural interpretation are aller au cinéma ‘to go to the movies’ (one or more visits) and venir chez toi ‘to come to your place. As we have seen, the use of beaucoup is fine in the context of these predicates. Beaucoup functions in these cases as an indication of the minimal cardinality of the pluralities that are taken into account: (32) a. Sylvie va beaucoup au cinéma. (= (25b)) b. Trois Allemands sont beaucoup venus chez toi. (= (28a)) Let us turn now to souvent and trois fois. The fact that these expressions take scope over an indefinite shows that their interpretation cannot depend on a plural interpretation of the predicate. The sentence in (30b) could be paraphrased as: the set of singular events defined by the predicate buying two kilos of olives is rather large. As souvent and trois fois contain a restriction, they are similar to quantified plural noun phrases, which obviously also take scope over indefinites: (33) Beaucoup de/trois personnes ont acheté deux kilos d’olives. a-lot of /three persons have bought two kilos of-olives ‘Many/three people bought two kilos of olives.’ In all cases where singular VP predicates are allowed, we are dealing with structures as in (30), where the singular VP defines the scope of a quantified phrase. Moreover, in all of these cases, plurality seems to be involved, the element fois ‘time/ times’, which is ambiguous between a singular and a plural, being interpreted as a plural.12 (34) Structures in which singular VP predicates are allowed a. [Q [abstract fois]] [scopeVP] b. [plusieurs [fois]] [scopeVP] c. [beaucoup [NPplural]] [scopeVP]

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This is in accordance with the claim that all essentially quantificational DPs, that is, those DPs that can take scope over an indefinite, are distributive (see Partee 1995, Szabolcsi 1997, Vanden Wyngaerd 1999). Our approach to Q-adverbs allows us to generalize this claim to expressions such as souvent and trois fois. Distributivity and plurality are conditions for scope taking. Souvent and trois fois can take scope because they contain a plural fois, which is abstract in the case of souvent, and overtly realised in the case of trois fois. At this point it is important to see that there is a difference between singular predicates such as to buy two kilos of olives and ‘once only’ predicates such as to write the letter, where the letter is a token. ‘Once only’ predicates cannot be interpreted as plurals because of the nature of the event they refer to. Once a letter has been written, it is there, and it cannot be written again, unless we talk about a letter type. As a result, ‘once only’ predicates are not only incompatible with beaucoup, but also with souvent. Both in Jean a beaucoup écrit cette lettre ‘Jean wrote this letter a lot’ and in Jean a souvent écrit cette lettre ‘Jean often wrote this letter’, the token interpretation of cette lettre ‘this letter’ is excluded. Singular predicates containing indefinites cannot have a plural interpretation, but this is not due to the impossibility of the described event to take place more than once. Predicates such as to buy two kilos of olives are singular, but nothing prevents the existence of two singular events in which two kilos of olives are bought. This is why quantification can result in a plurality of singular events, contrary to what we see in the case of ‘once only’ predicates, which are inherently singular. Beaucoup, which depends on the inherent possibility of a predicate to be interpreted as a plural (or a mass), is incompatible with both types of predicate. 4 [+RQ] and the availability of habitual readings The property [±RQ] is also responsible for certain distributional properties of Q expressions. As the examples in (35) show, only [+RQ] expressions allow for a habitual reading.13 The examples in (35) are fine and all have a habitual interpretation, which is related to the use of the present tense (see for instance De Swart 1991 for discussion). (35) a. Pierre va souvent au Louvre. ‘Pierre goes often to the Louvre.’ b. Pierre dort souvent. ‘Pierre sleeps often.’ c. Pierre va beaucoup au Louvre. ‘Pierre goes to the Louvre a lot.’

d. Pierre dort beaucoup. ‘Pierre sleeps a lot.’

The examples in (36), which contain [–RQ] expressions are either ininterpretable or they do not have the intended meaning. The example in (36c), for instance, means that Pierre is half asleep, and does not have the intended meaning, in which un peu modifies the quantity of sleeping. (36) a. #Pierre va trois fois au Louvre.

‘Pierre goes three times to-the Louvre.’ b. #Pierre va un peu au Louvre.

Pierre goes a bit to-the Louvre NOT: ‘Pierre goes from time to time to the Louvre.’

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c. Pierre dort un peu. Pierre sleeps a bit ‘Pierre is half asleep.’; NOT: ‘Pierre has the habit of sleeping now and then.’

As we have seen in section 2.2, [+RQ] expressions are dependent on a time interval whenever the quantity of reference with respect to which they are defined is within the scope of that time interval. [–RQ] expressions are interpreted independently of a time interval unless they are modified by an expression such as per week. This difference is the source of the contrast between the examples in (35) and (36). Habitual sentences characterise a time interval in a homogeneous way. In order for a habitual sentence to be true for a time interval X, it should be true for every subinterval of X as well which is sufficiently long to judge whether the sentence is true or not.14 As the interpretation of souvent and beaucoup varies with the time interval we pick, a habitual sentence containing souvent or beaucoup can be interpreted without any problem. The expressions trois fois and un peu are [–RQ] and as such they are interpreted independently of the time interval. This immediately explains the problem we have in interpreting these expressions in a habitual sentence. Consider again the example in (36a). Given an interval during which Pierre goes to the Louvre three times, there are many subintervals in which he does not go to the Louvre at all, or during which he goes to the Louvre twice or once. Thus, trois fois is incompatible with the homogeneous nature of the habitual. The same obtains for un peu. As we have seen in section 2.2, [+RQ] expressions do not need to be dependent on the time interval, while modified [–RQ] expressions can be. The first possibility is illustrated in (37) (cf (5a) and (8a)): (37) a. La semaine dernière/ Pendant sa jeunesse, Pierre est allé plus souvent au

Louvre que son grand-père (y est allé pendant toute sa vie). ‘Last week/ during his youth, Pierre went to the Louvre more often than his grandfather did during his whole life.’

b. La semaine dernière/ l’année dernière, il a plu davantage à Paris qu’il n’a plu à Amsterdam (depuis un an et demi). ‘Last week/ last year, it rained more in Paris than in Amsterdam during the past one and a half years.’

Depending on the presence or the absence of the part between brackets, the quantity of reference will be interpreted within or outside the scope of the time adverbial at the beginning of the sentence and of the habitual operator. We expect that the habitual reading is possible only in case the quantity of reference is within the scope of the habitual. The example in (38) shows, that this is in fact the case: (38) Pierre va au Louvre plus souvent/davantage que Jean (#y est allé l’année dernière). On the other hand, adding a modifier of the type par semaine or tous les après-midi makes a [–RQ] expression dependent on the time interval, as we have seen in (9), repeated here in (39): (39) a. L’année dernière/ Pendant sa jeunesse, Pierre est allé au Louvre trois fois

par semaine. ‘Last year/ During his youth, Pierre went to the Louvre three times a week.’

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b. La semaine dernière/L’année dernière, Pierre a dormi un peu tous les après-midi.

‘Last week/ last year, Pierre took a short nap every afternoon.’

As expected,[–RQ] expressions modified by expressions such as par semaine can be used in habitual sentences: (40) a. Pierre va au Louvre trois fois par semaine.

‘Pierre goes to the Louvre three times per week.’ b. Pierre dort un peu tous les après-midi.

‘Pierre has the habit of taking a short nap every afternoon.’ In this section we have seen how [±RQ] interacts with habituality. [+RQ] expressions can in principle be used in habitual sentences, unless they are interpreted with respect to a quantity of reference which is outside of the scope of the habitual operator, and which introduces a time interval of its own. [–RQ] expressions are normally incompatible with habitual readings, but can be modified in such a way that they become dependent on the time interval we pick. In that case, they can be used in habitual sentences. 5 Relational readings 5.1 The interaction between [±RQ] and [±QT] As we have seen above, frequency adverbs such as souvent have a further property that distinguishes them from all other Q-adverbs discussed in this paper: they allow for so-called relational readings (cf. De Swart 1991). Consider the following example, which has both a relational and a nonrelational reading (cf. (13)): (41) Quand il est à Paris, Pierre va souvent au Louvre.

RELATIONAL: ‘Often when he is in Paris, Pierre goes to the Louvre.’ NONRELATIONAL: ‘Whenever he is in Paris, Pierre goes often to the Louvre.’

In the relational reading, the sentence as a whole should be characterised as describing a state (cf. Partee 1983). This is clearly the case in (41), which is a habitual sentence. A state is true independently of the time interval one picks. As a result, a Q expression that allows for a relational reading should not be interpreted as an absolute quantity. As expected, the sentence in (42) cannot be interpreted as: ‘three of the times he is in Paris, Pierre goes to the Louvre’. Only the nonrelational reading, in which the Q expression is interpreted within the scope of the quand-clause is available. (42) Quand il est à Paris, Pierre va trois fois au Louvre. when he is in Paris Pierre goes three times to-the Louvre ‘Whenever he is in Paris, Pierre goes three times to the Louvre.’ (42) is in fact similar to (40a), where the x-times expression is modified by par semaine ‘per week’. In both cases the x-times expression is embedded under another quantifying expression. As a result, the number of times Pierre goes to the Louvre in a given time interval depends on the number of visits to Paris (in (41)) or the number of weeks (in (39a)) this interval contains. Because of this dependency on the time interval it is possible to use the [–RQ] expression in a habitual sentence. Given that the [–RQ] expression has to be within the scope of the quand-clause in order to allow for a stative interpretation, we expect the relational reading to be excluded. Adding par semaine ‘per week’ does not make the

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relational reading possible, as the x-times expression has to remain within the scope of par semaine: (43) only has a nonrelational reading. (43) Quand il est à Paris, Pierre va trois fois par semaine au Louvre. when he is in Paris Pierre goes three times per week to-the Louvre ‘Whenever he is in Paris, Pierre goes three times per week to the Louvre.’ The impossibility of (42) and (43) is directly due to the incompatibility of trois fois the habitual reading of the sentence. The use of the present tense excludes a nonstative interpretation and as such does not allow for the use of trois fois. This raises the question what happens in contexts where the simple past or “passé simple” is used. As shown by De Swart (1991), relational readings in French allow for the use of a passé simple: (44) A partir de ce jour-là, quand Marie rentra (PS), Pierre descendit (PS) toujours

l’escalier à sa rencontre. ‘From that day on, when Marie came home, Pierre always went down to meet her.’ The relational reading is, also in this context, excluded for trois fois. Interestingly, de Swart observes that tense must have wide scope with respect to the Q-adverb. This explains why the imperfect cannot be used in the consequent clause of (44), which would be possible in the absence of the Q-adverb. Consider the pair in (45): (45) a. Quand Marie rentra (PS), Paul descendait (IMP) l’escalier. ‘When Marie came home, Paul was going downstairs.’ b. Quand Marie rentra (PS), Paul monta (PS) l’escalier. ‘When Marie came home, Paul went downstairs.’ As the translations show, there is simultaneity between Marie’s coming home and Paul’s climbing the stairs in (45a), while in (45b) the two events happen in succession. Both readings are possible in (44). The relational reading blocks the possibility of disambiguation. As such, the simple past in (44) presents the relation as bounded, closed off in time. This suggests that first a state is created corresponding to “always (Marie rentrer) (Paul monter)”.15 The passé simple turns this state into an event (cf. Kamp & Rohrer 1983). If this is correct, the relational reading starts out with a stative interpretation, and can be turned into an eventive predicate by a simple past tense. Note that sentences such as (44) are not possible in for instance Spanish, where the use of the perfect tense requires preposing of the quantifier as in (46a) (cf. Menéndez-Benito 2002). Similarly, preposed trois fois allows for a reading in which it is outside of the scope of the quand-clause as in (46b) (Danièle Godard, p.c.). (46) a. Siempre que vino (PERF) a mi casa, Juan fumó (PERF). ‘Always when Juan came to my place, he smoked.’ b. Trois fois, quand il a plu, nous sommes allés au cinéma. ‘Three times, when it rained, we went to the movies.’ Here we only consider cases where the Q-adverb is within the consequent clause. We can conclude that Qs that allow the relational reading must be [+RQ], as they must be compatible with a stative interpretation.

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However, it is not the case that [+RQ] is a sufficient condition for allowing relational readings, given that beaucoup ‘a lot’ does not allow for a relational reading. As we have seen in section 2.1, beaucoup can be used in habitual contexts from which we can conclude that it has the property [+RQ]. (47) Quand il est à Paris, Pierre va beaucoup au Louvre. ‘When he is in Paris, Pierre goes to the Louvre a lot.’ NOT: ‘A lot of Pierres visits to Paris are visits during which Pierre goes to the Louvre.’ This shows us that relative quantity is not the only factor that determines the availability of the relational reading. I will argue that this difference between beaucoup and souvent can be understood in terms of [±QT] as well. Relational readings then depend on both [+RQ] and [+QT]. In the relational reading, the quand-clause determines how the restriction of Q is interpreted. In what preceded we adopted the idea, following Von Fintel (1994), that frequency adverbs contain a hidden domain anaphor. This domain anaphor is the target of pragmatic anaphora resolution, which means that it is filled in by the context and the situation in which the sentence is uttered. In a sentence such as John often beats Mary at ping-pong, often is restricted to situations in which John and Mary play ping-pong and probably also by some further contextual factors. This contextual restriction can be linguistically expressed in a when-clause. The when-clause functions as a topic, and as such identifies the domain anaphor contained in the frequency expression. In this respect Von Fintel’s approach differs from many other approaches in which the when-clause is seen as the semantic restrictor of the quantifier. Partee (1991) for instance, proposes a tripartite structure of quantification that obtains for determiners and adverbial Q expressions alike. when-clauses are parallel to NPs: (48) S Q Restriction Nuclear scope every happy student laughed often when it rains we play soccer Von Fintel argues that the schema in (48) may be a convenient meta-level notation. It is not the case however that the semantic (and syntactic) status of the noun phrase happy student with respect to the Q every is the same as that of when it rains with respect to often. Instead of Partee’s tripartite structure, Von Fintel argues in favour of the following schema: (49) S Q Restriction Nuclear scope every happy student laughed often domain anaphor we play soccer identified by: when it rains Within Partees view, the impossibility of having beaucoup in relational readings is not easily accounted for. Beaucoup can be interpreted with respect to an NP (cf. section 3.2). So if the quand-clause were similar to an NP, why would it be impossible to interpret beaucoup with respect to a quand-clause? Within Von Fintel’s approach, however, the quand-clause identifies the domain anaphor and it is not comparable to an NP which constitutes itself the

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restriction of the Q. The presence of the domain anaphor plays thus a crucial role in relating the Q expression and the quand-clause. As this anaphor is present in souvent and absent in beaucoup, we expect that relational readings are only possible in the context of souvent. In section 3 I adopted the idea that frequency adverbs contain a hidden element fois/times, which accounted for a number of properties of souvent. If we assume that fois can function as an anaphoric element which can be identified by a quand-clause, its presence allows us to account for the availability of relational readings in such a way that we can understand why this reading is not available for degree expressions such as beaucoup. Beaucoup lacks a hidden fois and is therefore incapable of introducing a relational reading. Given this analysis relational readings are predicted to be possible only in the context of a Q expression which is both [+RQ] and [+QT]. It has to be [+RQ] because the relational reading requires a stative interpretation, and it has to be [+QT] because the interpretation of the quand-clause depends on the presence of the domain anaphor present in frequency adverbs, and which directly correlates with its interpretation in terms of quantification over times. 5.2 Individual level predicates The difference between beaucoup and souvent discussed in the previous section sheds light on a number of interesting contrasts between beaucoup and souvent that have been observed by Obenauer (1983, 1984, 1994). In the context of certain predicates, beaucoup fails to get a quantitative interpretation, but the use of souvent is possible. In the examples in (50), beaucoup is completely excluded: (50) a. *Cette élève sait beaucoup la réponse. this student knows a lot the answer a’. Cette élève sait souvent la réponse. this student knows often the answer b. *Son jeu égale beaucoup celui de Lendl. her/his playing equals a-lot that of Lendl b’. Son jeu égale souvent celui de Lendl. her/his playing equals often that of Lendl In (51), beaucoup is allowed, but it can only be interpreted as an intensifier. The interpretation of the sentence is radically different depending on whether we use beaucoup or souvent: (51) a. J’ai beaucoup apprécié ses conseils. ‘I appreciated his advice a lot.’ a’. J’ai souvent apprécié ses conseils. ‘I often appreciated his advice.’ b. Son regard m’a beaucoup impressionné. ‘His glance impressed me a great deal.’ b’. Son regard m’a souvent impressionné. ‘His glance often impressed me.’ c. Cela a beaucoup accéléré la procédure. ‘That sped the procedure up a lot.’ c’. Cela a souvent accéléré la procédure. ‘That often sped the procedure.’ Un peu patterns with beaucoup while trois fois is excluded in all of these contexts.

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When looking more closely to these examples, it turns out that they all contain individual level predicates. This allows us to understand the contrasts, given the properties of Q expressions discussed in this paper. The absence of the quantity reading of beaucoup can be understood when we take into account the meaning of individual level predicates. According to de Swart (1991), the set of spatio-temporal locations that is associated with an individual-level or ‘once only’ predicate is a singleton set for all models and each assignment of individuals to the arguments of the predicate. As a result, they lack a quantitative scale to which beaucoup can be applied. One could say that the examples in (50) are similar to nonscalar adjectives, a context in which the use of beaucoup is blocked as well. In these cases the use of beaucoup is excluded, because the XP it modifies does not provide beaucoup with a scale to which it could be applied: (52) *peu/un peu dernier [nonscalar adjective ; cf. (50)]

little/ a little last

The predicates in (48) on the other hand resemble abstract nouns and scalar adjectives, both of which allow for modification by beaucoup, but not for the quantitative use of beaucoup, given the absence of a quantitative scale in their denotation: (53) a. beaucoup de plaisir [abstract noun ; cf. (51)] a-lot of pleasure b. peu/un peu difficile [scalar adjective ; cf. (48)] little/a bit difficult The observation that we are dealing with individual level predicates also accounts for the impossibility of trois fois. Given that we are dealing with ‘once only’ predicates, quantification is excluded. But what about souvent? First, it has to be noticed that souvent is in certain cases excluded in the context of predicates that disallow the quantitative use of beaucoup (note that the English translations of (54a-b) are as ungrammatical as their French counterparts):

(54) a. *Marie sait beaucoup parler français. ‘*Marie knows French a lot.’ a’. *Marie sait souvent parler français. ‘*Marie often knows French.’ b. *Jean et Pierre, son frère jumeau, se ressemblent souvent.

‘*Jean and his twin brother Pierre, resemble each other often.’ b’. Jean et Pierre, son frère jumeau, se ressemblent beaucoup.

‘Jean and his twin brother Pierre, resemble each other a lot (= strongly).’ The data in (54) follow if we take into account relational readings. Consider the well-known contrast in (55) (cf. Kratzer 1989): (55) a. *When Mary knows Frenchi, she often knows iti well.

b. When Mary knows a foreign languagei, she often knows iti well. (55b) has a relational reading. The when-clause contains an indefinite, which is the antecedent of a pronoun (a so-called donkey anaphor) in the consequent clause. This makes it possible for souvent to quantify over assignments: there is a set of events each of which is characterised as

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‘Mary knows x’ where x is a foreign language. For most of the members of this set, it obtains that ‘Mary knows x well’. As a result, the ‘once only’ character of savoir is circumvented. Turning back now to the examples of Obenauer in which souvent contrasts with beaucoup, we can observe that they all must have a relational reading and they all contain a donkey anaphor. This becomes clear when we look at the paraphrases of (50a’,b’) and (51a’-c’) in (56): (56) a. Often when a questioni is asked, she knows the answer to iti/that question.

b. Often when she plays tennis, her playing resembles that of Lendl. c. Often when she gave me advicei, I appreciated iti/the advice she gave. d. Often when I saw his looki, iti/ the look I saw impressed me.

e. Often when a procedurei was followed, that speeded iti up/ speeded up the procedure that was followed.

These are the only readings the sentences can have, and that is what we expect, given the presence of the individual level verb. 5.3 Relational readings, strength and iteration Relational readings do not implicate iteration of the main predicate. As we have seen in section 3.3, nonrelational souvent indicates that a given event took place many times. This is not the case, however, in the examples in (57), where we are dealing with a relational reading. In order to illustrate the point even more clearly, souvent is in these examples opposed to its antonym rarement. (57) a. Quand Pierre voit Sylvie, il est souvent de bonne humeur. ‘When Pierre sees Sylvie, he is often in a good mood.’ b. Quand Pierre voit Sylvie, il est rarement de bonne humeur. ‘When Pierre sees Sylvie, he is seldom in a good mood.’ The frequency adverb indicates the proportion of times at which Pierre sees Sylvie and he is in a good mood with respect to the number of times he sees her. The sentences do not implicate that the number of times Pierre is in a good mood is particularly important (souvent) or unimportant (rarement). Basically, we know very little about the number of times Pierre is in a good mood. In (57a), it is possible that he is hardly ever in a good mood, but that he usually gets in a good mood whenever he has the chance to run into Sylvie. On the other hand it might be that Pierre is constantly in a good mood, except for may be one of the times he saw Sylvie. Moreover, if Pierre saw Sylvie on Friday and on Saturday, and at both occasions he was in a good mood, the sentence does not give any information about Pierre’s mood in between these occasions. Similarly, (57b) can be true even though Pierre is very often in a good mood, except for the times when he runs into Sylvie. The opposition between the relational and the nonrelational reading of souvent is comparable to the opposition between the strong and weak reading of many (for a detailed comparison of meanings of frequency adverbs and determiners within the framework of generalized quantifiers, cf. De Swart 1991). Consider the sentences in (58): (58) a. There are many books in the library. b. Many of the books are interesting. There-sentences force a weak interpretation of many (cf. Milsark 1977). Partitives, as in (58b), only have a strong reading. In (58a), we are dealing with a large number of books. In (58b), however, many has a proportional reading. We have to take the proportion of books

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into account: a large proportion of a previously determined set of books is said to be interesting. Depending on the size of this set, we will determine what counts as many. In (57), the total number of times Pierre is in a good mood is left undetermined. Similarly, the sentence in (58b) does not say anything about the number of interesting things. A difference between the nominal and the verbal case is that the books in (58) necessarily coincide with interesting things, while the events in which Pierre sees Sylvie only overlap with situations in which Pierre is in a good mood. We can conclude that souvent is strong in relational sentences, while it is weak in nonrelational sentences. The inherently iterative reading of souvent (the ‘many times’ reading) is the weak reading. The strong reading does not say much about the number of times the event described in the consequent occurred. Certain frequency expressions, of which we would like to say that they have the property [+QT], only have a strong reading. This is for instance true for toujours ‘always’. Given that toujours ‘always’ involves universal quantification, and that universal quantification is necessarily strong, this is not surprising. Compare for instance the sentences in (59), which clearly do not have the same interpretation (see also section 5.4 below): (59) a. Jean regarde ma sœur tout le temps. ‘Jean looks at my sister all the time.’

b. Jean regarde toujours ma sœur. ‘Jean always looks at my sister.’

(59a) corresponds to a situation in which Jean keeps looking at my sister. (59b), on the other hand, describes a habit of Jean. He looks at my sister whenever he has the chance to do so. A question is whether this should be extended even to cases such as (60): (60) La porte est toujours ouverte. ‘The door is always open.’ According to De Swart (1991: 280), toujours is not a frequency expression in this context but a phase quantifier. As such, toujours in (60) can be assigned the following informal characterisation: ‘P is the case at the reference time R and indefinitely long before and afterwards.’ An alternative to De Swarts’ approach is to assume that we are in fact dealing with a relational reading in (60). Recall that in the examples in (57) the number of times in which Pierre is in a good mood is not defined. We do not need there to be a certain number of separate events in which Pierre is in a good mood. If we assume that in (60) the restriction of toujours is maximally general, this results in a continuous event of the door being open. This approach has an important advantage over the approach given in De Swart, as it allows us to generalize to a similar use of le plus souvent ‘usually’ and parfois ‘sometimes’: (61) a. La porte est le plus souvent ouverte. b. La porte est parfois ouverte.

‘The door is usually/sometimes open.’ The sentence in (61a) can be used to indicate that the chance to find the door open is rather large, which also suggests that we are dealing with a maximally general restriction of the quantifier. This can be illustrated by the fact that we can use (61a) in the following context:

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(62) Pierre forgot his sweater in Sylvie’s house. Jean tells him: Tu peux toujours essayer d’aller chercher ton pull dans la maison de Sylvie. Sa porte est le plus souvent ouverte, donc même si elle n’est pas là, tu pourras

probablement rentrer. ‘You can always try to get your sweater in Sylvie’s house. Her door is usually open, so even if she turns out to be absent, it will probably be possible to go inside.’

De Swart’s approach cannot be extended to le plus souvent, because the type of interpretation she uses only allows for one interval that is characterized by the predicate P, and not for several ones. The sentences in (61) introduces the conversational implicature that in some cases the door is closed. This in turn implies that there are several intervals characterised by P, and not a single one. 5.4 Independent readings and relational readings In the type of interpretation illustrated by the examples (60) and (61) above, toujours, parfois and le plus souvent are very close in their interpretation to temporal Q adverbs such as tout le temps ‘all the time’, de temps en temps ‘now and then’ and la plupart du temps ‘most of the time’. However, there is an interesting difference between these two classes of expressions in terms of dependency of the Q adverb with respect to a situation described in the preceding context, as shown by Molendijk & De Swart (1998). Frequency adverbs such as souvent and parfois introduce a so-called independent reading. This is illustrated in the fragment in (63): (63) Pauline et Jean jouent dans le jardin. Il la taquine souvent/parfois. Mais maintenant

(qu’ils jouent dans le jardin), il ne la taquine pas. ‘Pauline and Jean play in the garden. He teases her often/sometimes. But now (that they play in the garden), he does not tease her.’

The interpretation of souvent/parfois is not dependent on what is referred to in the first sentence. This is why the third sentence is appropriate in this context and does not lead to a contradiction. In this respect souvent and parfois differ from dependent quantifiers such as de temps en temps ‘from time to time’. De temps en temps necessarily refers back to a contextually determinable situation, which it qualifies globally. This can be illustrated by the fragment in (64). The second sentence, which contains de temps en temps, must be interpreted such that it globally qualifies the situation described in the first sentence. As a result, the third sentence of (64) leads to a contradiction: (64) Pauline et Jean jouent dans le jardin. De temps en temps, ils s’assoient dans

l’herbe. #Mais maintenant (qu’ils jouent dans le jardin), ils ne s’assoient pas dans l’herbe. ‘Pauline and Jean play in the garden. From time to time, they sit down in the grass. But now (that they play in the garden), they do not sit down in the grass.’

If we turn to degree adverbs that are compatible with the present tense, we can observe that they are similar to the dependent adverbs. Given that beaucoup is not felicitous in combination with small time intervals, we have to slightly adapt the example: (65) Pauline et Jean passent leur vacances au bord de la mer. Ils lisent beaucoup. #Mais

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maintenant (qu’ils passent leurs vacances au bord de la mer) ils ne lisent pas. ‘Pauline and Jean are on vacation at the sea side. They read a lot. But now (that they are on vacation at the sea side) they don’t read.’

A further observation about the dependent/nondependent contrast is, that the fragments become fine once we add normalement ‘normally’ or en général ‘in general’ in front of the sentence containing the dependent adverb. This shows that sentences containing the dependent adverb do not need to make global reference to a concrete situation. Independency seems to be correlated with the availability of the relational reading. De temps en temps is incompatible with relational readings, on a par with degree adverbs such as beaucoup: (66) Quand il est à Paris, Paul va de temps en temps au Louvre.

‘Whenever he is in Paris, Paul goes now and then to the Louvre.’ NOT: ‘Sometimes when he is in Paris, Paul goes to the Louvre.’

This suggests that the independent readings might be the result of the possiblity of triggering a relational reading, which allows us to give an account for the possibility of independent readings. The sentence containing parfois/souvent in (63) can be interpreted as follows: When they are together, or, alternatively, when they are playing together in the garden, Jean sometimes/often teases Pauline. This is expected, given that the domain anaphor corresponding to the restriction of parfois/souvent will be contextually identified. The antecedent of the domain anaphor cannot be a concrete, singular situation as this would result in vacuous quantification. As a result, the sentence containing souvent/parfois must be interpreted independently of the concrete situation described at the beginning of the fragment in (63). In the case of dependent quantifiers an ‘independent’ reading hinges on the explicit presence of a frequency term (normalement, en général), which allows us to accommodate a restriction and a different setting for the interpretation of the dependent adverb. In the previous section, we discussed the possibility of treating cases as La porte est toujours ouverte as instances of relational readings. In this view toujours is always relational. If it is true that relational readings are at the source of independent readings, while dependent readings are always nonrelational, we expect this type of sentence to have an independent reading only, which is correct. In the following fragment, toujours cannot mean: all of the time Pauline and Jean are playing in the garden. It is a general property of the door, independently of the situation described in the first sentence. (67) Pauline et Jean jouent dans le jardin. La porte de la maison est toujours ouverte. Ils

rentrent après une demi-heure. ‘Pauline and Jean play in the garden. The door of the house is always open. They get back in after half an hour.’

The discussion in this section shows that two properties are not enough to classify all Q-adverbs in French. Next to the four classes we investigated in detail in this paper, we have to distinguish at least a fifth class, corresponding to temporal Q-adverbs such as de temps en temps and la plupart du temps. Moreover, the property [+QT] should not be confused with temporal quantification. Expressions such as de temps en temps quantify over temporal intervals. The predicate indicates what happens at these intervals. In the logic of the account of relational readings offered here, these time intervals, contrary to fois, cannot be anaphoric to an event described in a when-clause, and therefore do not license relational readings. Thus temporal Q-adverbs differ from both degree adverbs and frequency adverbs. In the

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conclusions I will briefly speculate on the consequences of accomodating this fifth class of Q-adverbs within the system presented here. 6 Conclusions Beaucoup and souvent turn out to have in common that they are expressions of relative quantity or [+RQ]. As a result they can be used in habitual contexts. The property [+RQ] sets them apart from two other types of Q-adverbs that we have studied here: trois fois and un peu, both of which are [–RQ]. The differences between beaucoup and souvent are due to the fact that souvent quantifies over times, while beaucoup does not ([+QT] versus [–QT]). However, some contexts, such as the one in (1a,b) where beaucoup and souvent give rise to a very similar interpretation, cancel out this difference. It has been shown that the opposition between [±RQ] and [±QT] can account for a number of parallels and differences between four classes of Q-adverbs: frequency adverbs such as souvent, relative degree adverbs such as beaucoup, absolute degree adverbs such as un peu and x-times adverbs such as trois fois. The analysis makes clear why these classes of expressions have certain properties in common but not others. An important conclusion of the paper is that frequency adverbs (souvent) have to be distinguished from all other Q adverbs because they allow for relational readings. It has been argued that both properties, [+QT] and [+RQ], are involved in obtaining these readings. As a result of this, x-times adverbs (trois fois) and relative degree adverbs (beaucoup) pattern alike, but not because they have anything in common: whereas trois fois is [+QT] and [–RQ], beaucoup is [–QT] and [+RQ]. Thus the analysis shows that they are both incompatible with relational readings for different reasons. Relative degree adverbs and frequency adverbs have in common that they are expressions of relative quantity, which means that they are interpreted with respect to a contextually given ‘quantity of reference’. This makes them compatible with habitual readings. Frequency adverbs and x-times adverbs quantify over times and contain an abstract or overt plural element fois (their restriction); as a result they can quantify over indefinites. Degree adverbs indicate a degree. As such they can modify different categories: VPs, but also APs and NPs. Being devoid of a plural restriction, degree adverbs cannot take scope over an indefinite, unless they are used as a determiner of a plural DP. In the last part of the paper we have seen that the classification of adverbial Q expressions can be further extended in order to include temporal quantifiers such as de temps en temps, which are similar to both frequency adverbs and relative degree adverbs. We can speculate here about the way this should be done. Plausibly, inclusion of this class of Q-adverbs would imply a modification of the property [±QT]. [+QT] indicates both that there is a restriction and what the nature is of this restriction. It might be necessary to separate the presence of a restriction from the type of restriction. In that case we could say that degree adverbs lack a restriction, while frequency adverbs and temporal quantifiers contain a restriction. A difference in the type of restriction could then account for the differences between frequency adverbs and temporal quantifiers. Clearly this is an issue that needs further investigation. Another issue deserving further research concerns the cross-linguistic scope of the analysis. As stated in the introduction, the French facts are not typically French and not even typically Romance: the same patterns can be found in Germanic languages such as English and Dutch. This raises the question to what extent languages from other language families exhibit similar patterns as well.

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Doetjes, Jenny, Ad Neeleman & Hans van de Koot. 1998. Degree expressions and the autonomy of syntax. UCL Working Papers in Linguistics 10, 323-369.

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Notes ∗ This paper has been presented at various occasions: Going Romance 1999, an MA class at the French department of the Sorbonne, research seminars in Nijmegen and Utrecht, and a meeting with members of the PICS project group on adverbs. Besides the audiences of these presentations, I would like to thank Anne Abeillé, Lisa Cheng, Francis Corblin, Danièle Godard, Helen de Hoop, Fred Landman, Henriëtte de Swart, Hans Obenauer, Johan Rooryck and Elisabeth Villalta for their comments. The financial support of the Dutch Organisation for Scientific Research, NWO, is also gratefully acknowledged (NWO dossier 355-70-003). 1 This is one of the few examples in which English a lot differs from French beaucoup. See also note 10. 2 I will use the term adverb here without implying that we are dealing with single words and not with phrasal expressions. 3 Note that quelquesfois written in one word is a frequency adverb, and corresponds to English sometimes. Being a frequency adverb, quelquesfois is [+RQ] (cf. De Swart 1988). 4 The definition of relative quantity used in this paper differs from the one used by De Swart (1991). For De Swart, expressions that describe a relative quantity can be paraphrased in terms of ‘x times per time unit’. This definition cannot generalise over beaucoup and souvent, as it implies quantification over times. Moreover, her definition characterises a type of meaning, while our definition captures the property of a class of expressions which typically can get a certain type of meaning. For instance, le plus souvent is in our view always [+RQ], even though it can be interpreted independently of the time interval, as in (8a). 5 We do find elements that mean ‘large quantity’ or ‘small quantity’ as in French beaucoup (litt. ‘a good strike’)/ un peu ‘a little’ English a lot/ a bit and Dutch een hoop ‘a lot’ (litt. a heap)/ een beetje ‘a bit’. See Doetjes 1997:99-101 for discussion. 6 The reason I choose to talk about ‘times’ is morphological: this is the form we find in x-times adverbs and in many frequency adverbs. I use this term in the sense of situation or spatio-temporal location (but not in the sens of ‘time interval’, as will become clear in section 5.4). From a logical point of view, frequency adverbs can be used in contexts in which it seems inapproriate to talk about quantification over times (cf. Lewis 1975):

(i) A quadratic equation often has more than two solutions

Schubert and Pelletier (1989)argue against Lewis and state that, from a linguistic point of view, a tensed sentence is always tied to a particular time index, even when talking about atemporal objects such as quadratic equations (see also de Swart 1991 for discussion). The morphological properties of frequency adverbs such as sometimes point into the same direction. 7 Following Bach (1986), I assume that predicates such as to go to the Louvre are ambiguous between a singular and a plural reading. This idea will be elaborated in the next subsection. 8 David Lewis introduced the term ‘Universal Grinder’ in this context. The Universal Grinder produces mass nouns on the basis of any count noun that has physical objects in its extension. Gleason (1965) illustrates how context helps to make the shift possible for nouns such as shelf and book. A mother termite complains about her son, saying: ‘Johnny is very choosy about his food. He will eat book, but he won’t touch shelf.’ 9 In this section I only consider nonrelational readings. Cf. section 5 for a discussion of the interpretation of frequency adverbs in relational readings. 10 Note that English a lot can take scope over the indefinite, unlike its French counterpart beaucoup. This is not due to a systematic difference between English and French. Other pairs of a frequency adverb and a degree adverb exhibit the same pattern as the French data in the text, as illustrated by the pair more often-more in (i):

(i) a. John buys two kilos of olives more often than Peter does b. John buys two kilos of olives more than Peter does

The example in (ib) is ungrammatical in the intended reading: more, on a par with beaucoup, cannot take scope over an indefinite. This suggests that the difference is due to an exceptional property of a lot, which, at least in some contexts, can be interpreted as a lot of times. I will leave this issue aside. 11 Unless the degree expression is used as a real degree modifier, as in Pierre l’apprécie beaucoup ‘Pierre appreciates it/him a lot’. This type of examples will be discussed in section 5.2 below.

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12 According to Vanden Wyngaerd (1999), quantification and scope taking over an indefinites should be seen as instances of distributivity. Within this view, the scope properties of these expressions can be attributed to the presence of a plural expression in the restriction of the quantifier. 13 Cf. Ducrot (1979), Hoepelman & Rohrer (1980), Kleiber (1987) and De Swart (1991), who account for the opposition between souvent and trois fois in habitual contexts in a similar way. However, their analyses are restricted to the difference between souvent and trois fois: the adverbial use of beaucoup and un peu is not considered. 14 In the case of trois fois par semaine, we need minimally a time interval of a week. Similarly, if souvent aller au Louvre corresponds to a frequency of more than once a month, we need to look at sub-intervals of at least one month in order to judge whether the sentence is true. 15 As we will see below, this formal representation will be slightly modified.